From π to Pi

1

An Illustrated History of Computation

Bernie Cohen FBCS

Emeritus Professor of Computing City University

27/9/2013 ©2013 Prof Bernie Cohen OTA13

Computing in Antiquity

The Antikythera analog astronomical computer

(4thC BC) uses the Metonic (5thC BC) cycle:

19 solar years ≅ 235 synodic months

= 6940 days

Now I, even I, shall celebrate, in rhymes

inapt, the great immortal Syracusan ...(3rdC BC).

Showed that 31/7 < π < 310/71 and calculated the number

of grauns of sand in the unverse(= Eddington's

estimate of 1080 nucleons) without the use of zero.

Probably invented the Vitruvius (1stC BC)odometer: on each

rotation of the wheel. a pebble (calculus) dropped into a pot.

The number of pebbles determined the fare.

27/9/2013 ©2013 Prof Bernie Cohen OTA13 2

Victor 1, the first African Pope (189-199), fixed Easter on a Sunday in opposition to the

quartodeciman bishops of the Eastern Church.

Pope Paul I adopted a computus developed by the Scythian friar

Dionysius Exiguus (470–544) aka Dennis the Little

who also introduced the number zero into Europe and the notation BC/AD into the calendar (but made at least three errors that persist to this day!)

The Celtic Church had its own computus developed in Iona by

King Oswiu of Northumbria convened the

Synod of Whitby

in 664 to resolve the

conflict. The Celtic Church lost and

vanished until revived by the anti-papist Orange Order

1000 years later (hence the Irish Troubles!) St Columba


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When Computors Were Human

John Napier 1550 - 1617

and his bones

Blaise Pascal 1623 -1662 and his Pascaline The Brunswiga

1892-1959

The amazing Curta invented by Curt Herzstark

(1902 - 1988) while imprisoned in Buchenwald.

He survived because the Nazis wanted to give Hitler one for his birthday. After the war, he manufactured it in Lichtenstein at the invitation of

Prince Franz Jozef II.


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Navigation, Longitude and Time

Sextant and chronometer were useless without tables:

astronomical (here solar to sidereal time) and mathematical (logs, trig etc.). Human computors were trained to use

the 'method of differences' to interpolate between main values calculated by mathematicians.

In 1812, the high incidence of errors in these tables led ...


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Charles Babbage (1791 -1871)

to suggest to Sir John Herschel that they would be better

'constructed by steam' and he designed

the Difference Engine to do it. He soon realised that a machine

could be 'programmed' to do different calculations and designed

the Analytical Engine. He never completed it but

a detailed description written by Luigi Menebrea,

later Prime Minister of Italy, was translated and expanded with

example programs by the lady whom Babbage called the 'Enchantress of Numbers'

Augusta Ada Byron, Countess Lovelace

(1815-1852)


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The Theory of Computation

Alan Turing 1912 - 1954

Reframed Gödel's proof

using a universal model of

computation: the Turing Machine

David Hilbert 1862 - 1943

Hilbert's Programme: To prove that

mathematics is complete, consistent

and decidable.

John von Neumann 1903 - 1957

Polymath. Stored program

archiecture Self-replicating

automata

Alonzo Church 1903 - 1995 Ditto using a different, but equivalent model of

computation: λ-calculus

Kurt Gödel 1906 - 1978 Proved that mathematics

could not be both

complete and consistent

In 1934, Hilbert attended a banquet and was seated next to the new Minister of Education, Bernhard Rust. Rust asked, "How is mathematics in Göttingen now that it has been freed of the Jewish influence?

Hilbert replied, "Mathematics in Göttingen? There is really none any more."


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Prof John Rees 1918 – 2013 helped to break

Enigma 'Red' in 1940 using Turing's

Bombe

Colossus, built by ...

Breaking the Codes at Bletchley Park

When you leave valves on, they don't burn out.

Forbidden to work on ACE because of the OSA.

I can't tell you how to do it , but I wouldn't do it like that.

ca. 1966


to break Lorenz

Tommy Flowers 1905 – 1998

(BT Dollis Hill & STC)

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Ferranti Mark 1, 1951 the world's first commercially available electronic computer

Based on the 'Baby', designed in Victoria University, Manchester by Frank Williams

Early British Computers

Pilot ACE, 1946 designed by Turing for

NPL, Teddington

DEUCE, 1955 Made by English Electric

Nelson Research Lab, Stafford Based on ACE.

60 sold. This one was in Glasgow University in 1960.

STANTEC-ZEBRA, 1956

Zeer Eenvoudige Binaire Rekenautomaat

Made by STC, Newport designed by W. L. van der

Pool of Netherlands PTT


Replaced in 1964

by English Electric KDF9

runnning Algol 60.

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Ordered in October 1947 by Joe Lyons Tea Shops.

Ran the world's first regular routine office computer job in 1951.

At present four Government offices have been equipped with computers and orders have been placed for equipment for a further four. Studies of the possible use of

computers in five more offices have almost been completed. Jocelyn Simon, Financial Secretary to the Treasury,

House of Commons debate, June 26, 1958

Computers in Business

Ernest Kaye 1922-2012 Engineer and musician.

Last surviving member of the LEO I development team


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Programming Languages

The first program run on the'Baby',

predecessor of the Machester Mark 1 and

Ferranti Mark 1, Monday June 21,

1948.


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Programming Languages

Grace Murray Hopper, USN, 1906 - 1992 First compiler 1951

COBOL 1959

'DIVIDE CAKE INTO THREE'

John W Backus, IBM, 1924 - 2007

FORTRAN 1954

Peter Naur, U Copenhagen,

1928 - Algol 60

BNF : Backus-Naur Form syntactic metalanguage.

Panini (ca. 550BC) constructed a formal grammar of Sanskrit, the Ashtadhyayi

John G. Kemeny 1926 -1992

Dartmouth BASIC 1964. Manhattan Project with

John von Neumann. PhD under

Alonzo Church. Mathematical assistant

to Einstein.


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More Programming Languages Christopher Strachey 1916 - 1975 Scion of the Bloomsbury Group. Designed programming languages for Elliott and Ferranti. Creator of CPL, 'Christopher's Programming

Language', from which came BCPL, then B, then C, then Unix. First Prof of Computer Science at Oxford, founded denotational

semantics, the theory of programming languages.

John McCarthy 1927 -2011 Developed LISP at MIT in 1958: a Turing-complete language

with a few simple operators and a notation for functions, which provided the foundation for Artificial Intelligence.

Robin Milner, 1934 - 2010 City University, Ferranti, Cambridge, Edinburgh, Stanford, etc.

ML, CCS, LCF, pi-calculus. Automatic theorem proving Advised me not to take the Chair of IT at Surrey in 1984

as I would be more useful in industry. He was probably right.


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Minis and Mainframes

DEC PDP 8, 1965 up to 32K 12-bit words.

666KHz

IBM 360, 1964 Up to 8Mb 32-bit words, 1MHz

Courier Executerm 60, 1970 IBM 360 compatible remote terminal


DEC PDP 1, 1960 $120,000, up to 64K 18-bit words,

200KHz The first computer game:

Steve Russell's Spacewar! 20 bought by ITT for

ADX7300 message switch using Gordon Bell's UART.

The sad tale of the sheriff and the IBM sales

engineer

Chips with Everything

William Shockley 1910-1989

Nobel Laureate 1956 co-inventor with

Bardeen and Brattain of the contact

transistor at Bell Labs. Set up first 'Silicon Valley' company:

Beckman Instruments at Mountain View,

Palo Alto.

The first Fairchildren including Gordon Moore and Robert Noyce, founders of Intel,

left Beckman Instrunments in 1957 to form Fairchild Semicoductor, where they developed Silicon Gate Technolgy


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The Single Chip Microprocessor

Intel 8008, 1971 16Kb

in 8-bit words 3500

transistors 800KHz,

$120

Intel 4004. 1970, 4kB in 4-bit words, 2300 transistors, 740KHz, $200, designed for the NCM Busicom141-PF,


and signed 'FF', by Federico Faggin (1941 - )

who also designed the Intel 8008, 4040 and 8080. Disowned by Intel when he founded Zilog in 1974.


Carver Mead (1934 -)

Lynn Conway (1938 -)

The Bible and the Law

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VLSI (Very Large Scale Integration) and the Swiss Watch Industry

Self-Defeating Technology The Blundell Vector Slide Rule

(1952) and High Speed Electronic

Circuits


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Homebrew Computers

The MITS Altair 8800, 1975 $400 kits for electronics hobbyists.

10,000 kits shipped No software

Microsoft founded to supply a BASIC interpreter. CP/M OS added later.

Processor Technology Sol-20, 1977 'IBM Blue' case and walnut sides

Video and tape I/O interface boards built-in. Designed by Lee Felsenstein.

Kansas City data transfer standard.


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Xerox PARC

The Star, or Dandelion, outperformed the Sun but, at $16,595, was overpriced

and was abandoned as a product line by Xerox.


The Xerox 914 copier, 1959, generated so much profit that Xerox founded a non-profit

research lab in Palo Alto with instructions not to make product. Unfortunately they hired some crazy people who developed

the mouse, the graphical user interface and the ethernet

which they put together into the Alto personal computer, 1973

which inspired Steve Jobs to design the Apple and Stanford University to develop the Sun workstation.

The Alto was developed into the Xerox 8010 Star, 1981,

powered by a Symbolics LISP chip


Alan Kay 1940 -

1966: worked with Ivan Sutherland (1938 -) on Sketchpad (1962), the first GUI

The best way to predict the future is to invent it.

1968: worked with Seymour Papert(1928 -) on Logo 1973: worked in Xerox Parc with Doug Engelbart (1925-2013) on the mouse, and Adele Goldberg (1945 -) on Smalltalk, which became Squeak and Tweek,

In 1968, conceived Dynabook, prototype of the laptop, tablet and e-book reader, which became One Laptop Per Child.

1983: Chief Engineer at Atari then Apple then Disney, now Viewpoints Research Institute

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The 1977 Trinity

Apple II Commodore PET Tandy/Radio Shack TRS-80

Jack Tramiel 1928-2012 Commodore and Atari

Auschwitz survivor

Steve Jobs 1955-2012 Charles Tandy 1918-1978 Texas leather company


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Personal Computers

Atari 400, 1979 The original games machine

4 million sold IBM thought of buying the

company to get it, but instead designed ...

The IBM PC, 1981 4.77MHz Intel 8088, up to 256Kb RAM 2 floppy disk drives, open architecture

Operating system MS-DOS by Microsoft based on QDOS, based on CP/M

$1565


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Home Computers

Commodore 64, 1982 $595, 17 million sold

BBC Model A/B, 1981 Acorn (ARM)

£235, Millions sold

Sinclair ZX Spectrum, 1982 £125, 5 million sold

(not including clones)

Amstrad CPC464, 1984 £249, 3 million sold


Raspberry Pi, 2012 £20, ??? Sold

Sinclair ZX80, 1980 £99.99, 100,000 sold

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WIMP: the Xerox PARC Legacy

Apple Macintosh, 1984 8MHz Motorola 68000 MacPaint, MacWrite, Mac Draw 128k, $2495 256k, $2795

Windows 1.0 1985, 2 years late, slow and buggy Windows 2.0 1987 Mac look-alike, Aldus Pagemaker, Excel, Word, Corel Draw


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Meanwhile … on the telephone

Almon Brown Strowger

1839 - 1902 Undertaker

First exchange La Porte, IN, 1892

75 subscribers. First UK automatic

exchange Epsom, 1912

Alexander Graham Bell 1847 - 1922

Prof of Elocution. Founder of Bell Labs. Invented telephony,

aeronautics, hydrofoil and much else.

In 1876, the President of Western Electric declined to

buy Bell's patent for $100,000, claiming that the telephone was just a toy.

Two years later, he offered $2,000,000 for it.


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Digital telecoms

First digital telephone exchange Moorgate PCM, ITT-STC 1971 (now demolished and replaced by the 'ski slope' building in Fore St)

Alec Reeves 1902-1971 Pulse code modulation

STC 1937 Gottfried Ungerboeck

1940- Trellis coded modulation

IBM Zurich 1980 (now at Broadcom) Massively increased

transmission rates made data comms feasible.

Vint Cerf TCP/IP

on Arpanet DARPA 1972


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Convergence Tim Berners-Lee

CERN Hypertext,

1980 plus Internet

= WWW, 1989 Martin Cooper

Motorola DynaTac

('The Brick') 1973


Moses, meet Steve. He's going to upgrade

your tablet.

Meanwhile, on a different cloud ...


Recursion and Invariance

Dijkstra's Ball Game The Mutilated Chessboard


From π to Pi

Technology

Transcript of From π to Pi